The exact range from Earth is available on page 200 of
where the request "Do you have any idea where the S-IVB is with respect
to us?" occurs shortly after 7/18/69, GET 60:47, CDT 21:09, and the
mission commentary had just given the range as "184,600 nautical miles
from earth," about 212,000 statute miles, speed 2061 mph. The crew
was preparing for sleep after putting the CSM into a passive thermal
roll ["barbecue mode"] of 3 revs per hour, or about 18 deg/minute.
Elsewhere, Aldrin has discussed his role:
On Apollo 11 in route to the Moon, I observed a light out the window that appeared to be
moving alongside us. There were many explanations of what that could be, other than
another spacecraft from another country or another world – it was either the rocket
we had separated from, or the 4 panels that moved away when we extracted the lander
from the rocket and we were nose to nose with the two spacecraft. So in the close vicinity,
moving away, were 4 panels. And i feel absolutely convinced that we were looking at
the sun reflected off of one of these panels. Which one? I don’t know. So technically,
the definition could be “unidentified.”
We have telescopic observations of moon-bound Apollo spacecraft with
up to four flashing lights within a few tenths of an angular degree -- a few hundred miles at
those ranges. A summary of those observations and images is here:
and I attach one image from Apollo-13.
Mike Collins made the observation that he could just barely make out a shape
[that seemed to change] through the CM sextant's small telescope whose technical specs are here:
The instrument consisted of two telescopes. The first was a one-power, wide-field scanning telescope,
which was used to locate a star or constellation in space. The second was a 28-power sextant,
which took the actual reading.
The slow barbecue-mode roll would probably allow Collins to watch the flasher cross
the field of view, once he's lined it up to catch it every twenty minutes. Of course, they
could also watch it out a down-sun window. I don't know if the 28-power telescope was
removable from the sextant.
Something with just BARELY resolvable shape would be on the order of 0.01 deg across.
There were four SLA panels out there, 6.4 meters tall, about 3 meters wide at the apex,
and if they were at the range others were telescopically observed at on other missions,
they would be subtending visual angles of on the order of 0.001 degrees at about 100 miles out.
With a 28-power scope that puts it slightly above the physiological minimum to detect the existence
of a shape but not resolve it. Not proof, but comforting that it's consistent.
Recall the four panels would be distributed symmetrically around the CSM, but viewing
would only be possible from a shadowed window, so the fact that only one was seen
is not surprising.